Nonanalyticity of the beta-function and systematic errors in field-theoretic calculations of critical quantities

TL;DR

This paper examines how nonanalytic behavior of renormalization-group functions at fixed points affects the accuracy of numerical calculations of critical phenomena in field theory.

Contribution

It highlights the impact of nonanalyticity on systematic errors in fixed-dimension perturbative expansions for critical quantities.

Findings

Nonanalyticity causes systematic errors in numerical estimates.

Implications for improving precision in critical quantity calculations.

Analysis of fixed-dimension perturbative expansion limitations.

Abstract

We consider the fixed-dimension perturbative expansion. We discuss the nonanalyticity of the renormalization-group functions at the fixed point and its consequences for the numerical determination of critical quantities.